# UV complete me: Positivity Bounds for Particles with Spin

## TL;DR

This paper derives positivity bounds for particles with spin using transversity formalism, providing comprehensive constraints on effective field theories beyond the forward scattering limit.

## Contribution

It introduces a method to establish positivity bounds for particles with spin beyond the forward limit using transversity formalism, enhancing the constraints on effective theories.

## Key findings

- Derived positivity bounds for particles with spin using transversity formalism.
- Extended bounds beyond the forward scattering limit for all polarizations.
- Provided criteria to restrict effective field theory parameter space.

## Abstract

For a low energy effective theory to admit a standard local, unitary, analytic and Lorentz-invariant UV completion, its scattering amplitudes must satisfy certain inequalities. While these bounds are known in the forward limit for real polarizations, any extension beyond this for particles with nonzero spin is subtle due to their non-trivial crossing relations. Using the transversity formalism (i.e. spin projections orthogonal to the scattering plane), in which the crossing relations become diagonal, these inequalities can be derived for 2-to-2 scattering between any pair of massive particles, for a complete set of polarizations at and away from the forward scattering limit. This provides a set of powerful criteria which can be used to restrict the parameter space of any effective field theory, often considerably more so than its forward limit subset alone.